Dissipative dynamics of an open quantum battery

Coupling with an external environment inevitably affects the dynamics of a quantum system. Here, we consider how charging performances of a quantum battery, modelled as a two level system, are influenced by the presence of an Ohmic thermal reservoir. The latter is coupled to both longitudinal and transverse spin components of the quantum battery including decoherence and pure dephasing mechanisms. Charging and discharging dynamics of the quantum battery, subjected to a static driving, are obtained exploiting a proper mapping into the so-called spin-boson model. Analytic expressions for the time evolution of the energy stored in the weak coupling regime are presented relying on a systematic weak damping expansion. Here, decoherence and pure dephasing dissipative coupling are discussed in details. We argue that the former results in better charging performances, showing also interesting features reminiscent of the Lamb shift level splitting renormalization induced by the presence of the reservoir. Charging stability is also addressed, by monitoring the energy behaviour after the charging protocol has been switched off. This study presents a general framework to investigate relaxation effects, able to include also non Markovian effects, and it reveals the importance of controlling and, possibly, engineering system-bath coupling in the realization of quantum batteries.